432 Class 25
2024-04-23
Setup
Bonus Topic
OK, you ran a regression/fit a linear model and some of your variables are log-transformed.
- We fit a linear model to predict the log of an outcome. How might we most effectively interpret the coefficients of that model?
- How does our thinking change if we only take the log of a predictor?
- How about if we log both the outcome and the predictor?
Source is here for further reference (also see Class 25 README.)
Only the outcome is log-transformed
Exponentiate the coefficient. This gives the multiplicative factor for every one-unit increase in the independent variable.
- Example: the coefficient is 0.198. exp(0.198) = 1.218962. For every one-unit increase in the independent variable, our dependent variable increases by a factor of about 1.22, or 22%. Recall that multiplying a number by 1.22 is the same as increasing the number by 22%.
- Likewise, multiplying a number by, say 0.84, is the same as decreasing the number by 1 – 0.84 = 0.16, or 16%.
from this source
Only a predictor is log-transformed
Divide the coefficient by 100. This tells us that a 1% increase in the independent variable increases (or decreases) the dependent variable by (coefficient/100) units.
Example: the coefficient is 0.198. 0.198/100 = 0.00198. For every 1% increase in the independent variable, our dependent variable increases by about 0.002.
For x percent increase, multiply the coefficient by log(1.x).
Example: For every 10% increase in the independent variable, our dependent variable increases by about 0.198 * log(1.10) = 0.02
from this source
Both y and x are log-transformed
Interpret the coefficient as the percent increase in the dependent variable for every 1% increase in the independent variable.
- Example: the coefficient is 0.198. For every 1% increase in the independent variable, our dependent variable increases by about 0.20%.
- For x percent increase, calculate 1.x to the power of the coefficient, subtract 1, and multiply by 100.
- Example: For every 20% increase in the independent variable, our dependent variable increases by about (1.20 0.198 - 1) * 100 = 3.7 percent.
from this source
Today’s Main Topic
A brief introduction to …
- K-Means Clustering
- Principal Components Analysis
Examples:
- The 4000 biggest cities in the world
- The Palmer Penguins
- Arrest Rates in US States
Clustering the 4,000 Biggest Cities in the World
World Cities Data
- We’ll start with an example from section 9.1.2 of Baumer, Kaplan and Horton’s Modern Data Science with R.
BigCities <- world_cities |>
arrange(desc(population)) |>
head(4000) |>
select(longitude, latitude)
glimpse(BigCities)Rows: 4,000
Columns: 2
$ longitude <dbl> 121.45806, 28.94966, -58.37723, 72.88261, -99.12766, 116.397…
$ latitude <dbl> 31.22222, 41.01384, -34.61315, 19.07283, 19.42847, 39.90750,…Cluster by the 6-means algorithm
Map the cities and color by clusters
- The clustering algorithm has (essentially) identified the continents.
How does K-Means Clustering Work?
You can visit https://www.tidymodels.org/learn/statistics/k-means/ for a brief explanation of the clustering process using an animation from Allison Horst. Here, I’ll look at the pieces one slide at a time.
Allison’s materials are available at https://github.com/allisonhorst/stats-illustrations/tree/master/other-stats-artwork
From Allison Horst (1/11)
From Allison Horst (2/11)
From Allison Horst (3/11)
From Allison Horst (4/11)
From Allison Horst (5/11)
From Allison Horst (6/11)
From Allison Horst (7/11)
